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GLOBAL EXISTENCE FOR 3D NAVIER-STOKES EQUATIONS IN A THIN PERIODIC DOMAIN

  • Kwak, Min-Kyu (DEPARTMENT OF MATHEMATICS, CHONNAM NATIONAL UNIVERSITY) ;
  • Kim, Nam-Kwon (DEPARTMENT OF MATHEMATICS, CHOSUN UNIVERSITY)
  • Received : 2011.05.20
  • Accepted : 2011.06.05
  • Published : 2011.06.25

Abstract

We consider the global existence of strong solutions of the 3D incompressible Navier-Stokes equations in a thin periodic domain. We present a simple proof that a strong solution exists globally in time when the initial velocity in $H^1$ and the forcing function in $L^p$(0,${\infty}$;$L^2$), $2{\leq}p{\leq}{\infty}$ satisfy certain condition. This condition is basically similar to that by Iftimie and Raugel[7], which covers larger and larger initial data and forcing functions as the thickness of the domain ${\epsilon}$ tends to zero.

Acknowledgement

Supported by : Chonnam national university

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